Machine learning based signal recovery

ABSTRACT

Various aspects described herein relate to a machine learning based signal recovery. In one example, a computer-implemented method of noise contaminated signal recovery includes receiving, at a server, a first signal including a first portion and a second portion, the first portion indicative of data collected by a plurality of sensors, the second portion representing noise; performing a first denoising process on the first signal to filter out the noise to yield a first denoised signal; applying a machine learning model to determine a residual signal indicative of a difference between the first signal and the first denoised signal; and determining a second signal by adding the residual signal to the first denoised signal, the second signal comprising (i) signals of the first portion with higher magnitudes than the noise in the second portion, and (ii) signals of the first portion having lower magnitudes than the noise in the second portion.

RELATED APPLICATION DATA

This application claims priority to U.S. Provisional Application No.62/739,260 filed on Sep. 30, 2018, the entire content of which isincorporated herein by reference.

BACKGROUND 1. Field of the Invention

Aspects of the present inventive concept generally relate to recovery ofrelatively weak signals that are contaminated by noise and learnotherwise non recoverable using conventional processing methods.

2. Discussion of Related Art

Various types of data may be collected via use of one or a network ofvarious types of sensors such as audio sensors, cameras, etc. Examplesof such data can be seismic data collected in a field that can beanalyzed to understand surface/subsurface seismic activity, surfacetemperature data, weather data, traffic data, etc. Such data may becontaminated by noise during the collection process. Currently, variousconventional noise attenuation methods are utilized to recover signalsrepresenting the collected data. These conventional noise attenuationmethods often use different characteristics in frequency, wave number orother transform domains to separate the signals representing thecollected data from the noise. Examples of such noise attenuatingmethods include, but are not limited to, f-x projection filtering forrandom noise attenuation, a prediction error filtering to estimatecoherent signal in the f-x domain, using low-rank structure in the t-fdomain to attenuate ice-break noise, etc.

A shortcoming of all such noise attenuation methods is that they allinvolve a trade-off between preservation of the signals and the amountof filtered noise such that as noise attenuation increases, the targetsignals (e.g., seismic signals) are adversely affected. Moreover, somesignals are several orders of magnitude lower than the contaminatingnoise. Therefore, these signals are lost/eliminated together with thenoise during the filtering process, which adversely affect an accurateand complete analysis of the seismic data for underlying applications.

SUMMARY

The present inventive concept provides a system and method to extractsignals that represent underlying collected data from contaminatingnoise signals, and to prevent the loss of portions of such signals thatare several orders of magnitude smaller than the noise signals, whichmay be referred to as weak signals or relatively weak signals. Thesystem and method of the present inventive concept are operable to applymachine learning to preserve weak signals during a de-noising processfor extracting the signals.

In one aspect, a computer-implemented method of noise contaminatedsignal recovery includes receiving, at a server, a first signalincluding a first portion and a second portion, the first portionindicative of data collected by a plurality of sensors, the secondportion representing noise; performing a first denoising process on thefirst signal to remove the noise to yield a first denoised signal;applying a machine learning model to determine a residual signalindicative of a difference between the first signal and the firstdenoised signal; and determining a second signal by adding the residualsignal to the first denoised signal, the second signal comprising (i)signals of the first portion with higher magnitudes than the noise inthe second portion, and (ii) signals of the first portion having lowermagnitudes than the noise in the second portion.

In another aspect, the data corresponds to seismic data collected by theplurality of sensors.

In another aspect, determining the second signal is based on a singledictionary representing the noise trained using the machine learningmodel.

In another aspect, determining the second signal is based on a dualdictionary representing the noise and the data, the dual dictionarybeing trained using the machine learning model.

In another aspect, the method further includes training the machinelearning model with the first denoised signal every time the serverreceives a different instance of the first signal and determines acorresponding first denoised signal.

In another aspect, training the machine learning model includesdetermining a solution to an optimization problem using a k-singularvalue decomposition algorithm.

In another aspect, training the machine learning model is unsupervised.

In another aspect, determining the residual signal includes determininga solution to a dual domain sparse inversion problem using a sparserepresentation of the residual signal and the noise.

In another aspect, solving the dual domain sparse inversion problemincludes using a deterministic algorithm, the deterministic algorithmcorresponding to one of a nonmonotone alternating direction method, orstochastic algorithm such as matching pursuit.

In one aspect, a system for noise contaminated signal recovery includesmemory having computer-readable instruction stored therein, and one ormore processors. The one or more processors are configured to executethe computer-readable instructions to receive a signal contaminated bynoise, the signal including data collected by a plurality of sensors,the second portion representing noise; and process the signal using amachine learning model to yield a processed signal such that (1) thenoise is removed from the processed signal and (2) portions of the datawith magnitudes lower than magnitudes of the noise are preserved in theprocessed signal after removal of the noise.

In another aspect, the one or more processors are configured to executethe computer-readable instructions to process the signal by performing adenoising process on the signal to filter out the noise to yield adenoised signal; applying a machine learning model to determine aresidual signal indicative of a difference between the signal and thedenoised signal; and determining the processed signal by adding therecovered residual signal to the denoised signal.

In another aspect, the one or more processors are configured to controlthe plurality of sensors to determine the residual signal by determininga solution to a dual domain sparse inversion problem using a sparserepresentation of the residual signal and the noise.

In another aspect, solving the dual domain sparse inversion problemincludes using a deterministic algorithm, the deterministic algorithmcorresponding to one of a nonmonotone alternating direction method, orstochastic algorithm such as matching pursuit.

In another aspect, the one or more processors are configured to executethe computer-readable instructions to train the machine learning modelwith the denoised signal every time a different instance of the signalis received and a corresponding denoised signal is determined.

In another aspect, the one or more processors are configured to executethe computer-readable instructions to train the machine learning modelby determining a solution to an optimization problem using a k-singularvalue decomposition algorithm.

In another aspect, the one or more processors are configured to controlthe plurality of sensors to collect the data over a specified period oftime.

In one aspect, one or more non-transitory computer-readable medium havecomputer-readable instructions, which when executed by one or moreprocessors of a system for noise contaminated signal recovery, cause theone or more processors to receive a signal contaminated by noise, thesignal including data collected by a plurality of sensors, the secondportion representing noise; and process the signal using a machinelearning model to yield a processed signal such that (1) the noise isremoved from the processed signal and (2) portions of the data withmagnitudes lower than magnitudes of the noise are preserved in theprocessed signal after removal of the noise.

In another aspect, the execution of the computer-readable instructionsby the one or more processors, cause the one or more processors toprocess the signal by performing a denoising process on the signal tofilter out the noise to yield a denoised signal; applying a machinelearning model to determine a residual signal indicative of a differencebetween the signal and the denoised signal; and determining theprocessed signal by adding the recovered residual signal to the denoisedsignal.

In another aspect, the execution of the computer-readable instructionsby the one or more processors, cause the one or more processors tocontrol the plurality of sensors to determine the residual signal bydetermining a solution to a dual domain sparse inversion problem using asparse representation of the residual signal and the noise.

In another aspect, solving the dual domain sparse inversion problemincludes using a deterministic algorithm, the deterministic algorithmcorresponding to one of a nonmonotone alternating direction method, orstochastic algorithm such as matching pursuit.

In another aspect, the execution of the computer-readable instructionsby the one or more processors, cause the one or more processors to forma dataset using the signal and perform the denoising process on the dataset.

In another aspect, the execution of the computer-readable instructionsby the one or more processors, cause the one or more processors to trainthe machine learning model with the denoised signal every time adifferent instance of the signal is received and a correspondingdenoised signal is determined, by determining a solution to anoptimization problem using a k-singular value decomposition algorithm.

In another aspect, the data corresponds to seismic data collected by theplurality of sensors over a specified period of time.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the manner in which the above-recited and otheradvantages and features of the present inventive concept can beobtained, a more particular description of the principles brieflydescribed above will be rendered by reference to specific exampleembodiments thereof which are illustrated in the appended drawings.Understanding that these drawings depict only exemplary embodiments ofthe present inventive concept and are not therefore to be considered tobe limiting of its scope, the principles herein are described andexplained with additional specificity and detail through the use of theaccompanying drawings in which:

FIG. 1 illustrates an example environmental, according to an aspect ofthe present inventive concept;

FIG. 2 illustrates an example process for machine learning based signalrecovery, according to an aspect of the present inventive concept;

FIG. 3 illustrates example outputs of the process of FIG. 2, accordingto an aspect of the present inventive concept;

FIG. 4 illustrates example outputs of the process of FIG. 2, accordingto an aspect of the present inventive concept;

FIG. 5 illustrates example outputs of the process of FIG. 2, accordingto an aspect of the present inventive concept;

FIG. 6 illustrates example outputs of the process of FIG. 2, accordingto an aspect of the present inventive concept; and

FIG. 7 illustrates an example computing device, according to an aspectof the present inventive concept.

DETAILED DESCRIPTION

Various example embodiments of the present inventive concept arediscussed in detail herein. While specific implementations arediscussed, it should be understood that this is done for illustrationpurposes only. A person skilled in the relevant art will recognize thatother components and configurations may be used without parting from thespirit and scope of the present inventive concept. Thus, the followingdescription and drawings are illustrative and are not to be construed aslimiting. Numerous specific details are described to provide a thoroughunderstanding of the present inventive concept. However, in certaininstances, well-known or conventional details are not described in orderto avoid obscuring the description. References to one or an exampleembodiment of the present inventive concept can be references to thesame example embodiment or any example embodiment; and, such referencesmean at least one of the example embodiments.

Reference to “one embodiment” or “an embodiment” means that a particularfeature, structure, or characteristic described in connection with theexample embodiment is included in at least one example embodiment of thepresent inventive concept. The appearances of the phrase “in oneembodiment” in various places in the specification are not necessarilyall referring to the same example embodiment, nor are separate oralternative example embodiments mutually exclusive of other exampleembodiments. Moreover, various features are described which may beexhibited by some example embodiments and not by others.

The terms used in this specification generally have their ordinarymeanings in the art, within the context of the present inventiveconcept, and in the specific context where each term is used.Alternative language and synonyms may be used for any one or more of theterms discussed herein, and no special significance should be placedupon whether or not a term is elaborated or discussed herein. In somecases, synonyms for certain terms are provided. A recital of one or moresynonyms does not exclude the use of other synonyms. The use of examplesanywhere in this specification including examples of any terms discussedherein is illustrative only, and is not intended to further limit thescope and meaning of the present inventive concept or of any exampleterm. Likewise, the present inventive concept is not limited to variousexample embodiments given in this specification.

Without intent to limit the scope of the present inventive concept,examples of instruments, apparatus, methods and their related resultsaccording to the example embodiments of the present inventive conceptare given below. Note that titles or subtitles may be used in theexamples for convenience of a reader, which in no way should limit thescope of the present inventive concept. Unless otherwise defined,technical and scientific terms used herein have the meaning as commonlyunderstood by one of ordinary skill in the art to which the presentinventive concept pertains. In the case of conflict, the presentdocument, including definitions will control.

Additional features and advantages of the present inventive concept willbe set forth in the description which follows, and in part will beobvious from the description, or can be learned by practice of theherein disclosed principles. The features and advantages of the presentinventive concept can be realized and obtained by means of theinstruments and combinations particularly pointed out in the appendedclaims. These and other features of the present inventive concept willbecome more fully apparent from the following description and appendedclaims, or can be learned by the practice of the principles set forthherein.

Turning to FIG. 1, an example environmental according to an aspect ofthe present inventive concept is illustrated. Environment or setting 100illustrates a field 102 throughout which various types of sensors 104may be deployed to collect one or more types of data. For example, field102 may be a large geographical area over land, sea, air, etc. The oneor more types of data may include, but are not limited to, data onsurface/subsurface seismic activity, surface/subsurface temperatures,movements of objects such as animals, radioactive substances, waterflow, surface movement or displacement, etc.

Sensors 104 may be any type of known or to be developed device capableof collecting the underlying data including, but not limited to,conventional cameras, infrared cameras, audio/video sensors, etc. In oneexample, sensors 104 may be equipped with known or to be developedcomponents for communicating with other sensors and/or other networkcomponents such as access points 106 and/or processing center 110 (whichmay also be referred to as receiver 110 or server 110). These componentscan be wireless connection interfaces, ports for wired connection toother devices, etc.

Setting 100 further includes one or more access points 106, which mayinclude any type of known or to be developed access point such as awireless access point, a base station, a 4G/5G node B, etc.

Sensors 104 and access points 106 may communicate via any known or to bedeveloped wired and/or wireless communication schemes and protocols.

Access points 106 may be communicatively coupled to processing center110 via internet 108. Processing center 110 may be a single unit orcomprised of multiple units remotely placed from one another butcommunicatively coupled with one another. Processing center 110 mayfunction to provide a network operator with the capability to access,monitor, manage and maintain access points 106 and/or sensors 104, aswill be described below.

FIG. 2 illustrates an example process for machine learning based signalrecovery, according to an aspect of the present inventive concept. FIG.2 will be described from the perspective of processing center 110.However, it will be understood that processing center 110 has componentssuch as a processor and a memory (which will be described with referenceto FIG. 7), where such processor executes computer-readable instructionsstored on such memory to carry the functionalities described below withreference to FIG. 2. Additionally, processing center 200 may be a singleprocessor (CPU), a cluster of processors (CPUs), a cloud computingenvironment, etc.

At S200, processing center 110 may receive collected data from sensors104 via one or more of access points 106, as described above withreference to FIG. 1.

In one example, processing center 110 may configure sensors 104 tocollect such data continuously or for a specific period of time (e.g.,for 24 hours, 48 hours, a week, a month, etc.). The collected data maybe sent to processing center 110 by sensors 104 as a live stream as thedata is being collected or may be sent all at once after collection(e.g., after the data is collected for the specified period of time). Inanother example, a command send by processing center 110 to sensors 104may trigger transmission of the collected data from sensors 104 toprocessing center 110.

At S202, processing center 110 may group the collected data or portionsthereof together to create a dataset to be analyzed. This grouping ofthe collected data or portions thereof may be based on timestampsassociated with the received data. For example, when processing center110 receives the collected data continuously, at S202, processing center110 may select a portion of the data received over a specific period oftime (last 24 hours, 48 hours, week, month, etc.) into a dataset to beanalyzed.

In another example, sensors 104 may not be operating continuously. Forexample, processing center 110 may be able to turn them on and off. Assuch, processing center 110, prior to S200, may turn sensors 104 on,receive the collected data for a specific period of time, turn sensor104 off and then at S202 group the received data into a dataset. Thisdataset may be represented by d. d may be composed of a signal portion(desired signal representing the collected data), represented by u, anda noise portion representing either coherent noise or incoherent noisedepending on the noise type that contaminated the signal portion,represented by n. Accordingly, d may be given by formula (1) below:d=u+n  (1)

At S204, processing center 110 may perform an initial filtering(denoising) process for filtering out (removing) the noise portion tothe extent possible using any known or to be developedfiltering/denoising process. The signal portion after the initialfiltering process may be denoted as û (may be referred to as the initialfiltering result).

S204 results in a “clean” mode for training, therefore, a certain degreeof signal leakage is permissible. In one example, therefore, the initialfilter process may apply a simple filtering method due to theirefficiency such as an f-x deconvolution process or f-k filter withmoveout correction to filter the noise portion or any other known or tobe developed filtering methods or algorithms.

At S205, processing center 110, may rearrange (partition/divide) u intooverlapping patches and vectorizes each path. By exploiting theredundancy of seismic data, û may be expressed by a multiplication of adictionary D and sparse coefficient matrix x, per formula (2) shownbelow:û=Dx  (2)

As noted above, methods described herein to recover relatively weaksignals is based on applying machine learning. According to an exampleof such machine learning process, which may also be referred to as anunsupervised machine learning, a dictionary D may be trained using û.Accordingly, at S206, processing center 110 applies the initialfiltering result (û) to train dictionary D. In one example, trainingdictionary D is based on formula (2) below:min_(D,x) ∥û−Dx∥ _(F) ² s.t.∥x∥ ₀ ≤T.  (3)

In formula (3), T is a sparse threshold, T represents the sparsitythreshold, ∥⋅∥_(F) denotes the Frobenius norm, and ∥⋅∥₀, referred to asthe l₀ norm counts the number of nonzero entries. Formula (3) is anexample of an optimization problem can be solved using a K-SingularValue Decomposition (K-SVD) algorithm. Adopting the idea of blockcoordinate descent, the K-SVD algorithm can reduce the l₀ minimizationproblem into two subproblems—sparse coding and dictionary updating. Thesparse coding aspect includes calculating the sparse coefficientsthrough orthogonal matching pursuit (OMP) or a variant of OMP for agiven dictionary D, while the dictionary updating step updates atoms bysolving a series of rank-1 approximations to decrease the data misfit.Dictionary updating involves performing singular value decompositionrepeatedly. To reduce the complexity of dictionary learning, exactsingular value decomposition may be replaced with randomized singularvalue decomposition, or the solution thereof approximated by taking asingle iteration of gradient descent.

At S208, processing center 110 updates dictionary D with the solution tothe optimization problem given by formula (3). Accordingly, as more andmore data is collected, dictionary D is trained, which will then be usedto extract relatively weak signals that may otherwise be filtered withnoise using conventional noise filtering/attenuation processes. Theaccuracy of the residual signal recovery using dictionary D increases asmore and more data is used to train dictionary D.

At S210, processing center 110 stores the updated dictionary Din amemory or an associated database of processing center 110.

At S212, processing center 110 applies the stored dictionary D to derivea residual signal, which is a difference between d and û, given byformula (4) below:{circumflex over (d)}=d−û  (4)which denotes the residual signal with noise. For random Gaussian noise,we can employ a standard sparse inversion procedure for recovery. Thesparse representation of the residual signal, x₁, can be obtained bysolving:min_(x) ₁ ∥x ₁∥₁ s.t.∥{circumflex over (d)}−Dx ₁∥_(F) ²≤ϵ,  (5)where ϵ is the error threshold dictated by the noise variance, and ∥⋅∥₁denotes the l₁ norm used to impose sparsity with robustness. However,the assumption of Gaussian noise is rarely held for field data and,therefore, solving the standard sparse inversion problem may providesuboptimal results.

This residual signal, is a signal that contains the relatively weaksignals (e.g., weak seismic signal relative to the magnitude of thecontaminating noise signal) and therefore by applying dictionary Dthereto, the relatively weak signals can be recovered and added to û toobtain a final denoised signal. This final denoised signal has moresignals, including the relatively weak signals, retained therein, whencompared to the final denoised signals obtained by apply conventionalfiltering methods to d, as previously discussed.

In one example and in applying dictionary D, an assumption is made thatthe initial filtering result (i.e., û) and the residual signal (i.e.,{circumflex over (d)}) share the same set of basis functions.

In one example, to better separate the residual signal from the noise,processing center 110 may invert both (the residual signal and thenoise) simultaneously using a dual-domain sparse inversion processinggiven by formula (6) below:min_(x) ₁ _(,x) ₂ ∥x ₁∥₀ +α∥x ₂∥₀ s.t.∥{circumflex over (d)}−Dx ₁ −Sx₂∥_(F)≤ε  (6)

In formula (6), x₁ and x₂ are sparse representations of the residualsignal and the noise signal (i.e., e), S is the chosen sparsity basisfor the noise, ε is a configuration error tolerance, which may bedetermined according to experiments and/or empirical studies indicativeof the collected data (e.g., seismic data) and ∥x₁∥₀/∥x₂∥₀ may bereferred to as the l₀-norm. In one example, sparsity of the noise andresidual signals may be imposed using l₁-norm instead of l₀-norm.

With x₁ derived per formula (6), at S212, processing center 110 appliesD to x₁ to derive (determine) the residual signal (e.g., Dx₁).Thereafter, at S214, processing center 110 may determine a finalfiltered signal, which can be obtained by addition of Dx₁ to û. Thisfinal filtered signal may be referred to as u_(out) given by formula (7)below:u _(out) =û+Dx ₁  (7)

The final filtered (denoised) signal derived per process of FIG. 2 maybe used for further analysis of the underlying data for the intendedapplication (e.g., studying and understanding surface/subsurface seismicactivity, temperatures, weather pattern, etc.). This further processingmay be performed by processing center 110 or may be output by processingcenter 110 to another processing component for completing the furtheranalysis.

The above process described with reference to FIG. 2 may be referred toas signal recovery with single dictionary learning method. In anotherexample, a similar process but instead of one dictionary, there can be adual dictionary learning for signal recovery, where both noise andunderlying signal components are learned.

The proposed method of FIG. 2 with single dictionary learning demands apredefined S to characterize noise. It works well for incoherent noiseor well-behaved coherent noise, with energy focused in a transformdomain. However, the method with single dictionary training may not beoptimal or effectively represent the noise that is highly dispersive orscattered. A natural extension of the method is to build S by learningin a similar way and utilizes both adaptive dictionaries for invertingresidual signal.

For this dual dictionary training based method, assume that a noiseestimate can be attained by applying the conventional method, denoted byg; i.e.,{circumflex over (n)}=g(d).  (8)Next, the noise model 11 may be partitioned/rearranged in a same way asthe signal model û described above with reference to S205 of FIG. 2. Theformed noise matrix is then input to train the dictionary S by solving asimilar dictionary learning problem as in Formula (3) using the K-SVD.In the recovery step, the predefined transform is replaced by thetrained dictionary S adapted from the noise estimate. A similardual-domain sparse inversion as in formula (6) can be employed to invertthe residual signal from the noisy data a.

The dual dictionary learning may require additional estimate of thenoise model and one more training step prior to recovery, whichunavoidably increases the computation cost. However, the method providesan effective alternative for attenuating some of the most complex noise.

The proposed method with single or dual dictionary learning differs frommany residual signal recovery methods since it requires no assumptionson local similarities between the initial estimate and the residualsignal. A common set of bases functions in a global context suffices toassure the recovery.

One advantage of determining the final filtered signal per process ofFIG. 2 is that the process, unlike conventional filtering methods, doesnot need any assumption on neither local similarities nor signalcoherency in any transfer domain between the initial estimate and theresidual signal. In other words, a common set of base functions in aglobal context suffices to assure the success of signal recovery, whererelatively weak signals are preserved and as such, a more accurate andcomplete analysis of the received data can be performed.

FIG. 3 illustrates example outputs of the process of FIG. 2, accordingto an aspect of the present inventive concept. Graph 300 is an exampleof a noisy input received at S200 at processing center 110. Graph 302 isan example of the results of the initial filtering performed byprocessing center 110 on the received noisy input at S204. Graph 304 isan example of a difference between the noisy input of graph 300 and theinitial filtering result of graph 302 (e.g., {circumflex over (d)} performula (4) described above with reference to FIG. 2). Graph 306 is anexample of applying dictionary D to the residual signal (e.g., Dx₁).Graph 308 is an example of a subset of dictionary D with each patch(grid) in graph 308 representing an atom in the dictionary D. Finally,graph 310 is an example of u_(out) determined at S214, as describedabove.

FIG. 4 illustrates example outputs of the process of FIG. 2, accordingto an aspect of the present inventive concept. While FIG. 3 illustratesresults of applying the process of FIG. 2 to synthetic/computergenerated data, FIG. 4 illustrates the result of applying the process ofFIG. 2 to real world data collected on the Alaskan North Slope usingsensors 104 (e.g., point sources, point receivers as well as CompressiveSensing Imaging (CSI) technology). The collected data of FIG. 4 iscontaminated by strong noise due to extreme weather conditions withinthe region in which the data is collected.

The collected data is first sorted into offset-vector tiles (OVTs) shownin graph 400. According to process of FIG. 2 (i.e., S204) initialfiltering process is performed using Singular Spectrum Analysis (SSA) toreduce noise and generate initial signal estimate in the OVT domain.Graph 402 illustrates the collected data after the initial filterprocess of S204 using SSA while graph 404 illustrate the differencebetween graphs 400 and 402 (in other words, graph 404 illustrates theremoved noise).

Results of graph 402 is then fed into the above described dictionary toderive the residual signal shown in graph 406 (S206 to S212 of FIG. 2and using dual sparse inversion as described above). The process of S214is then applied to residual signals shown in graph 406 to provide thefinal filtered signal shown in graph 408.

Graph 410 illustrates the difference between the final denoised resultof graph 408 and the initial collected data shown in graph 400.

Comparing graphs 404 and 406, it can be observed that relatively weaksignals indicative of seismic activity are extracted with only afraction of noise remaining.

FIG. 5 example outputs of the process of FIG. 2, according to an aspectof the present inventive concept. FIG. 5 illustrates an example ofcoherent noise attenuation via dual dictionary learning as describedabove. High-density dataset over a producing field in Permian Basinusing CSI technology was taken. By applying the dual dictionarylearning, objective is to improve image quality for unconventionalreservoir development. The field from which data is taken is known to bea difficult seismic data area—salt dissolution in the near surface leadsto a strong back-scattering. Graph 500 exhibits a typical raw data, inwhich the scattered noise together with ground roll created a complexnoise pattern. In the near and mid offsets, the scattered energy is morethan 30 dB higher than the reflected energy

For initial noise attenuation, envelop soft mute followed by windowedFourier domain filtering (WFT) is employed to preserve flat or near-flatevents after static and moveout corrections. Graph 502 shows the initialdenoised result which was served as the signal estimate for training. Togenerate the initial noise estimate, envelop soft mute was applied againon the differences to extract the high-amplitude portion of thescattered and ground roll noise, as shown in graph 504. Both models arenext input for dictionary learning to adaptively form D and S, describedabove. Graphs 506 and 508 displays the subsets of learneddictionaries—atoms with distinct characters were trained which enablesfurther separation of signal and noise. Graph 510 shows the recoveredresidual signal by incorporating dual dictionaries in inversion, andgraph 512 shows the final denoised result with signal recovery.

We next stacked the data for further quality control (QC), the result ofwhich is shown in FIG. 6. FIG. 6 example outputs of the process of FIG.2, according to an aspect of the present inventive concept. Despite thehigh fold of over 10,000, the raw stack still exhibits strongdistortions from near-surface scattering, as shown in Graph 600. Graphs602, 604 and 606 plot the stacks of initial denoised data using WFT,recovered residual signal and final denoised data, respectively.Comparing Graphs 602 and 604, we can observe the primary energy has beensuccessfully recovered for both shallow and deep reflectors. The finaldenoised stack in Graph 606 indicates a good denoising quality withminimal distortions and primary leakage. Following a velocity modelbuilding exercise on denoised data, pre-stack depth migration wasperformed for imaging evaluation. Graphs 608 and 610 illustrate acomparison of a shallow migrated image (0-8,000 ft) between raw andfinal denoised data. The significant uplifts above 3,500 ft make thevery shallow image interpretable and allow better planning for hazardavoidance. The Delaware horizon (bright reflector around 4,500 ft) andbelow is also evidently better imaged, with reduced migration artifactsand clearly defined faults. The positive result from such a difficultdata area suggests a good performance of the proposed learning-basedmethod in attenuating coherent noise.

Signal recovery using single and dual dictionary learning are describedabove. However, the present disclosure is not limited thereto. Anynumber of N dictionaries may be used where N is a positive integergreater than 2 conditions on input signal being partitioned into Ndistinct signals/noises, where sparse invention can be applied to such Ndictionaries to recover underlying data signal.

Examples described above provide an unsupervised machine learning andsparse inversion based method for recovery of weak signals indicative ofseismic activity (weak relative to existing noise signals) that wouldotherwise be lost during noise filtering/attenuation process utilized bycurrent signal recovery methods. These examples are equally applicableto both coherent and incoherent noise on pre-stack and/or stackedimages.

Having described examples of machine learning based signal recovery withapplication to signals indicative of seismic activity and turning toFIG. 7, an example computing system 700 is illustrated, which can beimplemented as processing center 110 or a server of processing center110 for implementing functionalities described with reference to FIG. 2.System 700 can include components in electrical communication with eachother using a connection 705, such as a bus. System 700 includes aprocessing unit (CPU or processor) 710 and connection 705 that couplesvarious system components including the system memory 715, read onlymemory (ROM) 720 and/or random access memory (RAM) 725, to the processor710. System 700 can include a cache 712 of high-speed memory connecteddirectly with, in close proximity to, or integrated as part of processor710. System 700 can copy data from memory 715 and/or storage device 730to cache 712 for quick access by processor 710. In this way, cache 712can provide a performance boost that avoids processor 710 delays whilewaiting for data. These and other modules can control or be configuredto control processor 710 to perform various actions. Other system memory715 may be available for use as well. Memory 715 can include multipledifferent types of memory with different performance characteristics.Processor 710 can include any general purpose processor and a hardwareor software service, such as service 1 732, service 2 734, and service 3736 stored in storage device 730, configured to control processor 710 aswell as a special-purpose processor where software instructions areincorporated into the actual processor design. Processor 710 may be acompletely self-contained computing system, containing multiple cores orprocessors, a bus, memory controller, cache, etc. A multi-core processormay be symmetric or asymmetric.

To enable user interaction with system 700, an input device 745 canrepresent any number of input mechanisms, such as a microphone forspeech, a touch-sensitive screen for gesture or graphical input,keyboard, mouse, motion input, speech and so forth. An output device 735can also be one or more of a number of output mechanisms known to thoseof skill in the art. In some instances, multimodal systems can enable auser to provide multiple types of input to communicate with system 700.Communications interface 740 can generally govern and manage the userinput and system output. There is no restriction on operating on anyparticular hardware arrangement and therefore the basic features heremay easily be substituted for improved hardware or firmware arrangementsas they are developed.

Storage device 730 is a non-volatile memory and can be a hard disk orother types of computer readable media which can store data that areaccessible by a computer, such as magnetic cassettes, flash memorycards, solid state memory devices, digital versatile disks, cartridges,random access memories (RAMs) 725, read only memory (ROM) 720, andhybrids thereof.

Storage device 730 can include service 1 732, service 2 734 and/orservice 3 736 for execution by processor 710 to cause processor 710 tocarryout functionalities described above with reference to FIG. 2. Otherhardware or software modules are contemplated. Storage device 730 can beconnected to connection 705. In one aspect, a hardware module thatperforms a particular function can include the software component storedin a computer-readable medium in connection with the necessary hardwarecomponents, such as processor 710, connection 705, output device 735,and so forth, to carry out the function.

For clarity of explanation, in some instances the present technology maybe presented as including individual functional blocks includingfunctional blocks comprising devices, device components, steps orroutines in a method embodied in software, or combinations of hardwareand software.

In some embodiments the computer-readable storage devices, mediums, andmemories can include a cable or wireless signal containing a bit streamand the like. However, when mentioned, non-transitory computer-readablestorage media expressly exclude media such as energy, carrier signals,electromagnetic waves, and signals per se.

Methods according to the above-described examples can be implementedusing computer-executable instructions that are stored or otherwiseavailable from computer readable media. Such instructions can comprise,for example, instructions and data which cause or otherwise configure ageneral purpose computer, special purpose computer, or special purposeprocessing device to perform a certain function or group of functions.Portions of computer resources used can be accessible over a network.The computer executable instructions may be, for example, binaries,intermediate format instructions such as assembly language, firmware, orsource code. Examples of computer-readable media that may be used tostore instructions, information used, and/or information created duringmethods according to described examples include magnetic or opticaldisks, flash memory, USB devices provided with non-volatile memory,networked storage devices, and so on.

Devices implementing methods according to the present inventive conceptcan comprise hardware, firmware and/or software, and can take any of avariety of form factors. Typical examples of such form factors includelaptops, smart phones, small form factor personal computers, personaldigital assistants, rackmount devices, standalone devices, and so on.Functionality described herein also can be embodied in peripherals oradd-in cards. Such functionality can also be implemented on a circuitboard among different chips or different processes executing in a singledevice, by way of further example.

The instructions, media for conveying such instructions, computingresources for executing them, and other structures for supporting suchcomputing resources are means for providing the functions describedherein with respect to the present inventive concept.

Although a variety of examples and other information was used to explainaspects within the scope of the appended claims, no limitation of theclaims should be implied based on particular features or arrangements insuch examples, as one of ordinary skill would be able to use theseexamples to derive a wide variety of implementations. Further andalthough some subject matter may have been described in languagespecific to examples of structural features and/or method steps, it isto be understood that the subject matter defined in the appended claimsis not necessarily limited to these described features or acts. Forexample, such functionality can be distributed differently or performedin components other than those identified herein. Rather, the describedfeatures and steps are disclosed as examples of components of systemsand methods within the scope of the appended claims.

The previous description is provided to enable any person skilled in theart to practice the various aspects described herein. Variousmodifications to these aspects will be readily apparent to those skilledin the art, and the generic principles defined herein may be applied toother aspects. Thus, the claims are not intended to be limited to theaspects shown herein, but is to be accorded the full scope consistentwith the language of the claims, wherein reference to an element in thesingular is not intended to mean “one and only one” unless specificallyso stated, but rather “one or more.” Unless specifically statedotherwise, the term “some” refers to one or more. A phrase referring to“at least one of” a list of items in the claims and/or specificationrefers to any combination of those items, including single members ormultiple members. As an example, “at least one of a, b, and c” isintended to cover a; b; c; a and b; a and c; b and c; or a, b and c.

What is claimed is:
 1. A computer-implemented method of noisecontaminated signal recovery, the method comprising: receiving, at aserver, a first signal including a first portion and a second portion,the first portion indicative of data collected by a plurality ofsensors, the second portion representing noise; performing a firstdenoising process on the first signal to remove the noise to yield afirst denoised signal; applying a machine learning model to determine aresidual signal indicative of a difference between the first signal andthe first denoised signal; and determining a second signal by adding theresidual signal to the first denoised signal, the second signalcomprising (i) signals of the first portion with higher magnitudes thanthe noise in the second portion, and (ii) signals of the first portionhaving lower magnitudes than the noise in the second portion.
 2. Thecomputer-implemented method of claim 1, wherein the data corresponds toseismic data collected by the plurality of sensors.
 3. Thecomputer-implemented method of claim 1, further comprising: training themachine learning model with the first denoised signal every time theserver receives a different instance of the first signal and determinesa corresponding first denoised signal.
 4. The computer-implementedmethod of claim 3, wherein training the machine learning model includesdetermining a solution to an optimization problem using a k-singularvalue decomposition algorithm.
 5. The computer-implemented method ofclaim 3, wherein the training the machine learning model isunsupervised.
 6. The computer-implemented method of claim 1, whereindetermining the residual signal includes determining a solution to adual domain sparse inversion problem using a sparse representation ofthe residual signal and the noise.
 7. The computer-implemented method ofclaim 6, wherein solving the dual domain sparse inversion problemincludes using a deterministic algorithm, the deterministic algorithmcorresponding to one of a nonmonotone alternating direction method, orstochastic algorithm such as matching pursuit.
 8. The method of claim 1,wherein determining the second signal is based on a single dictionaryrepresenting the noise trained using the machine learning model.
 9. Themethod of claim 1, wherein determining the second signal is based on adual dictionary representing the noise and the data, the dual dictionarybeing trained using the machine learning model.
 10. A system for noisecontaminated signal recovery, the system comprising: memory havingcomputer-readable instruction stored therein; and one or more processorsconfigured to execute the computer-readable instructions to: receive asignal contaminated by noise, the signal including data collected by aplurality of sensors; and process the signal using a machine learningmodel to yield a processed signal such that (1) the noise is removedfrom the processed signal and (2) portions of the data with magnitudeslower than magnitudes of the noise are preserved in the processed signalafter removal of the noise.
 11. The system of claim 10, wherein the oneor more processors are configured to execute the computer-readableinstructions to process the signal by: performing a denoising process onthe signal to remove the noise to yield a denoised signal; applying themachine learning model to determine a residual signal indicative of adifference between the signal and the denoised signal; and determining aprocessed signal by adding the residual signal to the denoised signal.12. The system of claim 11, wherein the one or more processors areconfigured to control the plurality of sensors to determine the residualsignal by determining a solution to a dual domain sparse inversionproblem using a sparse representation of the residual signal and thenoise.
 13. The system of claim 11, wherein the one or more processorsare configured to execute the computer-readable instructions to: trainthe machine learning model with the denoised signal every time adifferent instance of the signal is received and a correspondingdenoised signal is determined.
 14. The system of claim 13, wherein theone or more processors are configured to execute the computer-readableinstructions to train the machine learning model by determining asolution to an optimization problem using a k-singular valuedecomposition algorithm.
 15. The system of claim 13, wherein trainingthe machine learning model is unsupervised.
 16. The system of claim 10,wherein the data corresponds to seismic data collected by the pluralityof sensors.
 17. The system of claim 16, wherein the one or moreprocessors are configured to control the plurality of sensors to collectthe data over a specified period of time.
 18. One or more non-transitorycomputer-readable medium having computer-readable instructions, whichwhen executed by one or more processors of a system for noisecontaminated signal recovery, cause the one or more processors to:receive a signal contaminated by noise, the signal including datacollected by a plurality of sensors; and process the signal using amachine learning model to yield a processed signal such that (1) thenoise is removed from the processed signal and (2) portions of the datawith magnitudes lower than magnitudes of the noise are preserved in theprocessed signal after removal of the noise.
 19. The one or morenon-transitory computer-readable medium of claim 18, wherein theexecution of the computer-readable instructions by the one or moreprocessors, cause the one or more processors to process the signal by:performing a denoising process on the signal to remove the noise toyield a denoised signal; applying the machine learning model todetermine a residual signal indicative of a difference between thesignal and the denoised signal; and determining a processed signal byadding the residual signal to the denoised signal.
 20. The one or morenon-transitory computer-readable medium of claim 19, wherein theexecution of the computer-readable instructions by the one or moreprocessors, cause the one or more processors to control the plurality ofsensors to determine the residual signal by determining a solution to adual domain sparse inversion problem using a sparse representation ofthe residual signal and the noise.
 21. The one or more non-transitorycomputer-readable medium of claim 20, wherein solving the dual domainsparse inversion problem includes using a deterministic algorithm, thedeterministic algorithm corresponding to one of a nonmonotonealternating direction method, or stochastic algorithm such as matchingpursuit.
 22. The one or more non-transitory computer-readable medium ofclaim 21, wherein the execution of the computer-readable instructions bythe one or more processors, cause the one or more processors to form adataset using the signal and perform the denoising process on the dataset.
 23. The one or more non-transitory computer-readable medium ofclaim 19, wherein the execution of the computer-readable instructions bythe one or more processors, cause the one or more processors to: trainthe machine learning model with the denoised signal every time adifferent instance of the signal is received and a correspondingdenoised signal is determined, by determining a solution to anoptimization problem using a k-singular value decomposition algorithm.24. The one or more non-transitory computer-readable medium of claim 18,wherein the data corresponds to seismic data collected by the pluralityof sensors over a specified period of time.